Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers. Since C× is abelian, it follows that T is as well. The circle group is also the group U(1) of 1×1 unitary matrices; these act on the complex plane by rotation about the origin. The circle group can be parametrized by the angle θ of rotation by This is the exponential map for the circle group.
primaryTopic
Circle group
In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers. Since C× is abelian, it follows that T is as well. The circle group is also the group U(1) of 1×1 unitary matrices; these act on the complex plane by rotation about the origin. The circle group can be parametrized by the angle θ of rotation by This is the exponential map for the circle group.
has abstract
(унитарная группа порядка 1) в ...... го вещественного пространства.
@ru
Die Kreisgruppe oder Torusgrup ...... keiner Drehung identifiziert.
@de
El grupo circular o U(1) es el ...... plejos es decir, si entonces .
@es
Grupa okręgu – podgrupa 𝕋 gru ...... , skąd pochodzi oznaczenie 𝕋.
@pl
In de wiskunde is de cirkelgro ...... rking is de vermenigvuldiging.
@nl
In matematica, il gruppo circo ...... circolare è quindi un 1-toro.
@it
In mathematics, the circle gro ...... ) is geometrically an n-torus.
@en
زمرة الدائرة (بالإنجليزية: Cir ...... دة للمستوي العقدي تعطى بالشكل:
@ar
在數學裡，圓群標記為T，為所有模為1之複數所組成的乘法群，即 ...... 積）幾何上是個n-環面的此一事實。而圓群即正是一個1-環面。
@zh
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(унитарная группа порядка 1) в ...... го вещественного пространства.
@ru
Die Kreisgruppe oder Torusgrup ...... keiner Drehung identifiziert.
@de
El grupo circular o U(1) es el ...... plejos es decir, si entonces .
@es
Grupa okręgu – podgrupa 𝕋 gru ...... otną rolę w teorii grup Liego.
@pl
In de wiskunde is de cirkelgro ...... rking is de vermenigvuldiging.
@nl
In matematica, il gruppo circo ...... circolare è quindi un 1-toro.
@it
In mathematics, the circle gro ...... tial map for the circle group.
@en
زمرة الدائرة (بالإنجليزية: Cir ...... دة للمستوي العقدي تعطى بالشكل:
@ar
在數學裡，圓群標記為T，為所有模為1之複數所組成的乘法群，即 ...... 積）幾何上是個n-環面的此一事實。而圓群即正是一個1-環面。
@zh
label
Circle group
@en
Cirkelgroep
@nl
Grupa okręgu
@pl
Grupo circular
@es
Gruppo circolare
@it
Kreisgruppe
@de
U(1)
@ru
زمرة الدائرة
@ar
圓群
@zh
